Without any transmit spectral shaping, the analog downstream signal of a PCM modem can encounter the following analog impairments:
A. Inability to pass low frequency (DC) content of the downstream signal due to analog circuitry used for DC loop signaling; PA0 B. Inability to pass high frequency (near 4000 Hz) content of the downstream signal due to both the shape of the central office PCM anti-imaging filter and analog loop characteristics; PA0 C. Excessive non-linear distortion caused by significant low frequency energy in the transmit signal; and PA0 D. Single frequency injection (50 Hz/60 Hz) within the analog channel which may cause performance degradation. PA0 A. Separate the set L of all valid transmit PCM values into N subsets. All N subsets contains one or more symbols of L. No subset contains symbols that are within any other subset. For example, the most discussed method has L/2 subsets, each subset containing a positive and negative value of the same magnitude; PA0 B. Select a particular subset of the possible N subsets from the transmitted bits; and PA0 C. Select one of the plurality of symbols within the selected subset based upon minimizing a cost function. Most frequently the cost function is a running digital sum (RDS).
Various methods have been proposed to shape the PCM downstream transmit spectrum. These methods are essentially variants of the following approach:
The primary problem with the above approach is the selection of the necessary amount of symbol redundancy to achieve the desired transmit spectrum. If the sign of the selected symbols is used, 1 bit of transmit signal is lost due to shaping. This fixed amount of symbol redundancy may be too much for simple spectral shaping or too little for complex spectral shaping requirements.